United led for 88 minutes at Goodison Park thanks to Zlatan Ibrahimovic's first-half effort. Fellaini was brought off the bench with five minutes of the match remaining to try and help his side hold onto their lead, but less than two minutes later he brought down Idrissa Gueye in the penalty box.
Mourinho was quizzed on the incident by Sky Sports in his post-match interview but refused to answer the question. The United boss was also asked about the first-half incident where Marcos Rojo could have easily been shown a straight red card for a two footed lunge on Gueye, but again, refused to comment.
In his post-match press conference, Mourinho was pushed further on Fellaini's woeful contribution and explained he decided to introduce the former Everton midfielder in a bid to combat the Toffees' "direct" style of football.
"Everton is not the passing team anymore, like they were," Mourinho said, the Manchester Evening News report. "Everton is a team that plays direct, everything is direct, goalkeeper: direct, Ashley Williams; direct, Funes Mori; direct. Everything is direct.
"And when a team is losing and plays direct, intensifies the direct football, and when you have a player on the bench with two meters you play the player in front of the defensive line to help the team to (win) the match."
United have won just twice in the league since late September – against struggling Leicester City and Swansea City - and now sit nine points off fourth place Manchester City - and 13 off league leaders Chelsea.